Let $c$ Be a Positive Number $\frac { d y } { d t } = k y ^ { 1 + c }$

question 19

Multiple Choice

Let $c$ be a positive number. A differential equation of the form $\frac { d y } { d t } = k y ^ { 1 + c }$ where $k$ is a positive constant is called a doomsday equation because the exponent in the expression $k y ^ { 1 + c }$ is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term $k y ^ { 100 }$ . If 3 such rabbits breed initially and the warren has 27 rabbits after 3 months, then when is doomsday?

• A) \(47.03\) months
• B) \(97.03\) months
• C) \(67.03\) months
• D) \(137.03\) months
• E) \(117.03\) months

---

Definitions:

Minority Status

A social position occupied by a group of people in a society who are fewer in number or who are marginalized or discriminated against.

Generational Immigrant

Refers to members of an immigrant family that belong to different generations, highlighting the differing experiences and adaptations among family members across generations.

Connectedness

The state or quality of being connected or interconnected, especially regarding social relationships and emotional bonds.

Mutuality

A mutual relationship or connection between two or more parties where both sides benefit or are affected equally.